Elasticity explores the fundamental concepts of stress and strain in materials, detailing how they return to their original shape after deformation. It covers essential terms such as tensile stress, compressive stress, and shear stress, along with the corresponding types of strain. This resource is ideal for students studying physics or engineering, providing clear explanations and formulas related to elasticity, including Hooke's Law and Young's Modulus. It also discusses practical applications in construction and material selection.

Key Points

  • Explains the concepts of stress and strain in materials, including tensile and compressive stress.
  • Covers Hooke's Law and its significance in understanding material elasticity.
  • Details Young's Modulus and its applications in engineering and construction.
  • Discusses the differences between ductile and brittle materials in terms of elasticity.
ybishop2554
13 pages
Language:English
Type:Textbook
Biology
ybishop2554
13 pages
Language:English
Type:Textbook
Biology
250
/ 13
1
ELASTICITY
Elasticity is the property of a material by virtue of which it regains its original shape and size after
the removal of the deforming force, provided the elastic limit is not exceeded. Materials such as
steel, rubber, and glass exhibit elastic behaviour within certain limits.
BASIC TERMS IN ELASTICITY
1. Stress
Stress is the restoring force per unit area developed inside a body when an external force is applied.
Stress
Force
Area
SI Unit: Pascal (Pa) or N/m²
Pa N/m
Types of Stress
1. Tensile Stress
Tensile stress is the stress produced in a material when forces act to stretch or elongate it.
2. Compressive Stress
Compressive stress is the stress produced in a material when forces act to compress or
shorten it.
3. Shear Stress
Shear stress is the stress produced when tangential forces act parallel to a surface, causing
one layer of the material to slide over another.
4. Bulk Stress
Bulk stress is the stress produced when a body is subjected to uniform pressure from all
directions, resulting in a volume change.
2. Strain
Strain is the fractional change in dimension produced by stress.
Compressive force
Tensile force
2
Strain
Change in dimension
Original dimension
Strain has no unit because it is a ratio (dimensionless quantity).
Types of Strain
1. Longitudinal Strain
Longitudinal strain is the ratio of the change in length of a material to its original length
when subjected to tensile or compressive stress.
Longitudinal Strain

2. Shear Strain
Shear strain is the angular deformation produced in a material due to shear stress.
Consider a rectangular block fixed at the bottom, with a tangential force acting on its top
surface. Initially, the block is rectangular . After applying the shear force, the top
surface shifts slightly, and the block becomes 
󰆒
󰆒
.
Let:
= height of the block, = lateral displacement of the top surface, = angle of deformation
(shear angle)
From geometry:

But shear strain is defined as:
Shear Strain
Lateral displacement
Height
Hence,
Shear Strain

For very small deformations, the angle is very small (measured in radians).
Using the small-angle approximation:

Volume Strain
Volume strain is the ratio of the change in volume of a body to its original volume.
A
B
A
C
A
D
A
󰆒
󰆒
3
Volume Strain

HOOKE’S LAW

Statement of Hooke’s Law
Within the elastic limit, stress is directly proportional to strain.
Stress Strain
Stress Strain
where:
= modulus of elasticity (elastic constant)
For a spring:

where:
= applied force, = spring constant, = extension or compression
Elastic Limit
The elastic limit is the maximum stress a material can withstand and still return to its original shape
when the load is removed. Beyond this limit, permanent deformation occurs.
MODULUS OF ELASTICITY
The modulus of elasticity is the ratio of stress to strain. It measures the stiffness of a material.
Modulus
Stress
Strain
YOUNG’S MODULUS
Young’s modulus is the ratio of longitudinal stress to longitudinal strain within the elastic limit.
Longitudinal Stress
Longitudinal Strain




where:
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Figures

Elasticity: Understanding Stress and Strain Concepts — Applications of Bulk Modulus

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FAQs

What is elasticity in materials science?
Elasticity is the property of a material that allows it to regain its original shape and size after the removal of a deforming force, provided the elastic limit is not exceeded. Materials such as steel, rubber, and glass exhibit elastic behavior within certain limits. This property is crucial for understanding how materials respond to external forces and is foundational in fields like engineering and physics.

What are the types of stress in materials?
There are four primary types of stress in materials: tensile stress, compressive stress, shear stress, and bulk stress. Tensile stress occurs when forces act to stretch or elongate a material, while compressive stress results from forces that compress or shorten it. Shear stress is produced when tangential forces act parallel to a surface, causing one layer of the material to slide over another. Bulk stress occurs when a body is subjected to uniform pressure from all directions, leading to a change in volume.

How is strain defined in the context of elasticity?
Strain is defined as the fractional change in dimension produced by stress, calculated as the change in dimension divided by the original dimension. It is a dimensionless quantity, meaning it has no units. The two main types of strain discussed are longitudinal strain, which relates to changes in length, and shear strain, which describes angular deformation due to shear stress.

What is Hooke's Law and its significance?
Hooke's Law states that within the elastic limit, stress is directly proportional to strain. This relationship can be expressed as Stress = E × Strain, where E is the modulus of elasticity. Hooke's Law is significant because it provides a foundational understanding of how materials behave under load, allowing engineers to predict material performance in various applications.

What are the applications of Young's Modulus?
Young's Modulus is utilized in several practical applications, including the construction of bridges and buildings, the selection of materials for engineering works, and the design of wires and rods. It measures the stiffness of a material by defining the relationship between longitudinal stress and longitudinal strain, which is critical for ensuring structural integrity and performance in engineering designs.

What is the difference between ductile and brittle materials?
Ductile materials can undergo large plastic deformation before breaking, allowing them to be stretched into wires. They typically exhibit large elongation before fracture and are considered tough. In contrast, brittle materials fracture suddenly with little or no plastic deformation, breaking easily under stress and showing very small deformation before fracture. Examples of ductile materials include copper and aluminum, while glass and cast iron are examples of brittle materials.

What is the significance of the stress-strain curve?
The stress-strain curve is significant because it illustrates the relationship between stress and strain for a material, highlighting important regions such as the proportional limit, elastic limit, yield point, ultimate tensile stress, and breaking point. This curve helps engineers determine the strength of materials and select suitable materials for various applications, ensuring that structures can withstand applied forces without failing.